Details

Time bar (total: 20.2s)

sample108.0ms

Algorithm
intervals
Results
33.0ms47×body1280valid
20.0ms39×body640valid
16.0ms138×body80valid
8.0ms25×body320valid
2.0ms7×body160valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
313524
420624
549124
6330124
done500024

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* 2.0 J) (cos (/ K 2.0)))
0.4b
(* (* -2.0 J) (cos (/ K 2.0)))
5.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite397.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
23×add-exp-log add-cbrt-cube
13×*-un-lft-identity associate-*r*
12×pow-prod-down prod-exp cbrt-unprod
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
4×sqrt-div add-log-exp
3×associate-*l* *-commutative
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 79
Calls
4 calls:
26.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
40.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
231.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
97.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series654.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
63.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
300.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
219.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.5s

Counts
91 → 91
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01371776
13631596
222251387
done50011385

prune471.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.1b

localize33.0ms

Local error

Found 4 expressions with local error:

2.5b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.6b
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* -2.0 (* J (cos (/ K 2.0)))))
10.8b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.8b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×pow1
13×add-exp-log cbrt-prod add-cbrt-cube
11×add-sqr-sqrt
9×add-cube-cbrt
7×sqrt-prod
6×cbrt-div pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×flip3-+ pow1/3 associate-*l* flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*r* *-commutative
Counts
4 → 70
Calls
4 calls:
73.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
58.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* -2.0 (* J (cos (/ K 2.0)))))
33.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
35.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
331.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
164.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* -2.0 (* J (cos (/ K 2.0)))))
296.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
357.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify966.0ms

Counts
82 → 82
Iterations

Useful iterations: done (961.0ms)

IterNodesCost
01562275
13532138
213171858
done50011803

prune587.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.1b

localize41.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* -2.0 (* J (cos (/ K 2.0)))))
5.5b
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.8b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×pow1
13×add-exp-log add-cbrt-cube
11×cbrt-prod
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
6×pow-prod-down prod-exp cbrt-unprod
4×cbrt-div sqrt-div add-log-exp
3×flip3-+ associate-*l* flip-+ distribute-lft-out
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 68
Calls
4 calls:
69.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* -2.0 (* J (cos (/ K 2.0)))))
37.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
81.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
46.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* -2.0 (* J (cos (/ K 2.0)))))
364.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
229.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
286.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify913.0ms

Counts
80 → 80
Iterations

Useful iterations: done (910.0ms)

IterNodesCost
01702241
13792095
214281818
done50001800

prune663.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 9.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
0.4b
(* (* 2.0 J) (cos (/ K 2.0)))
5.5b
(* (* -2.0 J) (* (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cos (/ K 2.0))))
7.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
23×pow1
21×add-cbrt-cube
14×prod-exp
11×*-un-lft-identity pow-prod-down cbrt-unprod
10×add-sqr-sqrt
9×add-cube-cbrt
7×unpow-prod-down
4×sqrt-div associate-*r* pow-exp sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*r/ associate-*l* associate-*l/ *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 82
Calls
4 calls:
43.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
40.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
147.0ms
(* (* -2.0 J) (* (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cos (/ K 2.0))))
96.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series735.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
54.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
285.0ms
(* (* -2.0 J) (* (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cos (/ K 2.0))))
200.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts
94 → 94
Iterations

Useful iterations: 2 (475.0ms)

IterNodesCost
02001999
15511791
224201577
done50001577

prune364.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.1b

regimes319.0ms

Accuracy

16% (8.1b remaining)

Error of 16.7b against oracle of 8.5b and baseline of 18.2b

bsearch205.0ms

Steps
ItersRangePoint
6
3.077919292655663e-223
3.916434144326975e-222
1.0069196441333906e-222
9
-7.819917765711077e-224
-3.0391354023161685e-230
-5.928674869168629e-224

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03581
14781
done4781

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.5s1529×body1280valid
935.0ms4302×body80valid
799.0ms1263×body640valid
304.0ms581×body320valid
119.0ms328×body160valid